不可积多态Landau-Zener模型中绝热性随隧穿能隙增加的损失
Loss of adiabaticity with increasing tunneling gap in non-integrable multistate Landau-Zener models
摘要：
我们考虑了最简单的多态Landau-Zener跃迁的不可积模型。在该模型中，两个隧道耦合量子点中的两对能级被栅极电压扫过。虽然这个2 * 2模型是不可积的，但当能级间的能量距离远小于它们的隧道分裂时，它可以在极限下解析求解。结果与类似的2 * 1模型形成对比，其中一个点仅包含一个水平。后者模型不允许虚拟跃迁振幅的干扰，并且它是完全可解的。在2 * 1模型中，对于在时间t -> - \infty处在一个点中的粒子，在时间t-> \infty处在同一点中的概率随着隧道耦合而指数地下降。相比之下，在2 * 2模型中，这种概率随着隧道耦合呈指数增长。这种增长的物理起源是在两个点系统中形成隧道诱导的集体态。这可以看作是迪克效应的一种表现。
英文摘要：
We consider the simplest non-integrable model of multistate Landau-Zener transition. In this model two pairs of levels in two tunnel coupled quantum dots are swept passed each other by the gate voltage. Although this 2 * 2 model is non-integrable, it can be solved analytically in the limit when the inter-level energy distance is much smaller than their tunnel splitting. The result is contrasted to the similar 2 * 1 model, in which one of the dots contains only one level. The latter model does not allow interference of the virtual transition amplitudes, and it is exactly solvable. In 2 * 1 model, the probability for a particle, residing at time t -> -\infty in one dot, to remain in the same dot at t -> \infty falls off exponentially with tunnel coupling. By contrast, in 2 * 2 model, this probability grows exponentially with tunnel coupling. The physical origin of this growth is the formation of the tunneling-induced collective states in the system of two dots. This can be viewed as manifestation of the Dicke effect.
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